Nonlinear anomalous diffusion equation and fractal dimension: Exact generalized Gaussian solution
Nonlinear anomalous diffusion equation and fractal dimension: Exact generalized Gaussian solution
In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation $\ensuremath{\partial}\ensuremath{\rho}/\ensuremath{\partial}t=\mathbf{\ensuremath{\nabla}}\ensuremath{\cdot}(K\mathbf{\ensuremath{\nabla}}{\ensuremath{\rho}}^{\ensuremath{\nu}})\ensuremath{-}\mathbf{\ensuremath{\nabla}}\ensuremath{\cdot}(\ensuremath{\mu}\mathbf{F}\ensuremath{\rho})\ensuremath{-}\ensuremath{\alpha}\ensuremath{\rho},$ where ${K=Dr}^{\ensuremath{-}\ensuremath{\theta}},$ $\ensuremath{\nu},$ $\ensuremath{\theta},$ $\ensuremath{\mu},$ and D are real parameters, F is the external force, and $\ensuremath{\alpha}$ is a …